The housekeeper and the professor

'Well, let's see'!
How can you be so nonchalant? It'll be dark soon!"

---

I was wrong, there would be no revelations about the number 10, it
seemed. In this case, 10 was the age of a small boy, and nothing more.
"It's all right," I said. "He does this every day."
"Every day! You abandon your son every day so you can come here to
make hamburgers?"
"I don't abandon him, and it's my job to come here." I wasn't sure why the
Professor was so concerned about my son, but I went back to my recipe,
adding some pepper and nutmeg.
"Who takes care of him when you're not home? Does your husband come
home early from work? Does his grandmother watch him?"
"No, unfortunately there's no husband or grandmother. It's just the two of
us."
"So he's at home all alone? He sits and waits for his mother in a dark
house while you're here making dinner for a stranger? Making 
my
dinner!"
No longer able to control himself, the Professor jumped up from his chair
and began circling the table. The notes on his body trembled as he ran his
hand nervously through his hair. Dandruff sprinkled on his shoulder. I
turned off the soup just as it began to boil.
"You really don't need to worry," I said, trying to sound calm. "We've
been doing this since he was much younger. Now that he's ten, he can
manage for himself. He has the phone number here, and if he needs help, he
knows to ask the landlord downstairs—"
"No, no, no!" The Professor cut me off as he paced around the table. "You
should 
never
leave a child alone. What if the heater fell over and started a
fire? What if he choked on a candy? Who'd be there to help? Oh! I don't
want to think about it. Go home right now! You should make dinner for
your child. Go home!" He grabbed my arm and tried to pull me toward the
door.
"I'll go," I said, "but I just have to make these hamburgers for you."

---

"Are you going to stand there frying hamburgers while your child could
be dying in a fire? Now listen to me: beginning tomorrow you'll bring your
son along with you. He can come straight here from school. He can do his
homework, and be near his mother. And don't think you can fool me just
because I'll forget by tomorrow."
He pulled off the tag that read "the new housekeeper" and fished a pencil
from his pocket. Under the portrait, he added the words "and her son, ten
years old."
I left that evening—or rather, I was chased out—without having time to
wash my hands, let alone clean the kitchen properly. The Professor
appeared even angrier than when I had interrupted his thinking. But his
anger seemed to hide a deep fear, and I hurried home wondering what I
would do if I found the apartment in flames.
Any reticence or wariness I felt for the Professor vanished the moment I
saw him with my son, and from that point on I trusted him completely. As
I'd promised the evening before, I gave my son a map to the house and told
him to come directly from school. It was against agency rules to bring
children to the workplace, but there was no denying the Professor.
When my son appeared at the door the next day with his schoolbag on his
back, the Professor broke into a wide grin and opened his arms to embrace
him. I didn't even have time to point at the line he'd added to his note—"and
her son, ten years old." As a mother, it was a joy to see someone so
completely embrace my child, and I felt a slight twinge of jealousy that my
welcome from the Professor was always much more reserved.
"I'm so glad you've come!" he said, without any of the questions he asked
me every morning. Bewildered by the unexpected greeting, my son
stiffened, but managed a polite answer. The Professor took off my son's
Hanshin Tigers baseball cap and rubbed his head. Then he gave him the
nickname before he'd even learned his real one.

---

"I'm going to call you Root," he said. "The square root sign is a generous
symbol, it gives shelter to all the numbers." And he quickly took off the
note on his sleeve and made the addition: "The new housekeeper ... and her
son, ten years old, 
."
At first I made us name tags, thinking that if the Professor weren't the
only one with notes clipped to him he might feel less anxious. I told my son
to change his school name tag for one I made that read "
." The
experiment proved less successful than I'd hoped. No matter how much
time passed, I was always the young woman who made painfully slow
progress with numbers, and my son would be the boy who simply appeared,
and was embraced.
My son soon grew accustomed to the Professor's enthusiastic greeting and
even came to enjoy it. He would take off his cap at the door and present the
flat top of his head, as if to show how proud he was to be worthy of the
name Root. And for his part, the Professor never missed his cue, he
mentioned the square root whenever he met my son.
My contract stipulated that I would make dinner for him at six o'clock and
leave at seven after finishing the dishes; but the Professor began objecting
to this schedule as soon as my son arrived on the scene.
"I won't stand for it! If you have to finish here and then make another
meal once you get home, Root won't get his dinner until eight o'clock. That
just won't do. It's inefficient; it's illogical. Children should be in bed by
eight o'clock. You can't deprive a child of his sleep—that's when he does his
growing."
For a mathematician, his argument wasn't very scientific, but I decided to
ask the director of the agency if it would be possible to deduct the cost of
our dinner from my salary.
The Professor had never before thanked me for my efforts in the kitchen,
but his attitude changed when the three of us sat down to dinner together for
the first time. His manners were exemplary. He sat up very straight and ate
quietly, without spilling so much as a drop of his soup on the table or his

---

napkin—all of which seemed odd, given how terrible his manners had been
when it was just the two of us.
"What's the name of your school?" he asked.
"Is your teacher nice?
"How was lunch today?
"What do you want to be when you grow up?"
As he squeezed lemon on his chicken or picked out the carrots from his
soup, the Professor would ask Root one question after another, without
hesitating, even when the question concerned the past or the future. He was
determined to make our dinner hour as peaceful and pleasant as possible.
Though Root's answers to his questions were mostly perfunctory, the
Professor listened attentively, and it was thanks to his efforts that we ate
together without drifting into any awkward silences.
He was not simply humoring a child. Whenever Root would put his
elbows on the table or clatter his dishes or commit any other breach of
etiquette (all things the Professor had done himself at his earlier solitary
meals), the Professor would gently correct him.
"You have to eat more," he said one evening. "A child's job is to grow."
"I'm the shortest one in my class," said Root.
"Don't let that bother you. You're storing up energy, pretty soon you'll
have a growth spurt. One of these days, you're going to feel your bones
begin to stretch out and grow."
"Did that happen to you?" Root wanted to know.
"No, unfortunately, in my case, all that energy was wasted on other
things."
"What other things?"
"On my friends. I had some very close friends, but as it turned out they
weren't the sort you could play baseball or kick-the-can with. In fact,
playing with them didn't involve moving at all."

---

"Were your friends sick?"
"Just the opposite. They were big and strong as a rock. But since they
lived in my head, I could only play with them there. So I ended up growing
a strong brain instead of a strong body."
"I see," said Root. "Your friends were numbers. My mom says you're a
great math teacher."
"You're a bright boy. Very bright. That's correct, numbers were my only
friends.... But that's why you need to get lots of exercise while you're
young. Do you understand? And you have to eat everything on your plate,
even the things you don't like. And if you're still hungry, you can have
anything on my plate, too."
"Thanks!"
Root had never enjoyed dinner as much as he did when we ate with the
Professor. He answered the Professor's questions and let him fill his plate to
overflowing, and whenever he could, he looked curiously around the room
or stole a glance at the notes on the Professor's suit.
Root was a child who had rarely been embraced. When I first saw him in
the hospital nursery, I felt something closer to fear than to joy. His eyelids
and earlobes and even his feet were still swollen and damp from the
amniotic fluid. His eyes were half-closed, but he didn't seem to be asleep.
His tiny arms and legs, protruding awkwardly from the oversized gown,
flailed from time to time as if in protest at having been left here by mistake.
I was eighteen, ignorant, and alone. My cheeks were sunken from
morning sickness that had continued right up to the moment I lay down on
the delivery table. My hair stank with sweat, and my pajamas were still
stained where my water had broken.
There were fifteen babies in the nursery and he was the only one awake. It
was before dawn and the halls were empty except for the women at the
nurse's station. His fists had been clenched tight, but at that moment he
opened them, and then awkwardly bent them closed again. The small

---

fingernails were dark and discolored with traces of what I assumed was my
blood.
"Excuse me," I called, staggering down to the nurse's station. "I'd like to
cut my baby's fingernails. He seems to be moving his hands a lot and I'm
afraid he'll scratch himself...." Perhaps I was trying to convince myself that
I was a good mother.
From the time of my earliest memories, I had no father. My mother had
fallen in love with a man she could never marry, and she had raised me by
herself. She worked at a reception hall that people hired for weddings. She
had started out helping wherever she was needed—bookkeeping, dressing
the wedding parties, flower arranging, table coordination—and ended up
managing the whole place.
She was a strong woman who hated nothing more than having people
think of her daughter as poor and fatherless. Though we were, in fact, poor,
she did her best to make us look and feel rich. She asked the women who
worked in the dressmaking department to give us scraps of material from
which she made all my clothes. She arranged for the organist at the hall to
give me piano lessons at a discount. And she brought home the leftover
flowers and made pretty arrangements for the apartment.
I suppose I became a housekeeper because I kept house for my mother
from the time I was a small child. When I was barely two and not quite
potty trained, I would wash out my own panties if I had an accident; and
before I was even in elementary school, I was using the knives in the
kitchen and cutting up the ingredients to make fried rice. By the time I was
ten, I not only took care of the whole apartment, but I was even paying the
electric bill and attending meetings of the neighborhood association in my
mother's place.
My mother never said a word against my father and always insisted he
was a fine man and terribly handsome. He managed a restaurant
somewhere, but the specifics were always kept from me. I was given to

---

understand, however, that he was tall, fluent in English, and a connoisseur
of opera.
The image I have of my father is that of a statue in a museum. No matter
how close I come to him, I can't get his attention, he continues to stare off
into the distance without looking down, and he never reaches out his hand
to me.
It wasn't until I entered adolescence that it occurred to me how odd it was
that the wonderful man my mother described had abandoned us and had
never offered even the least bit of economic support. But by that time I had
no interest in learning more about him, and I accepted the role of silent
accomplice when it came to my mother's illusions.
It was my pregnancy that utterly destroyed those illusions, along with the
others she'd carefully stitched together from fabric scraps, piano lessons,
and leftover flowers. It happened not long after I'd started my junior year of
high school.
The boy was someone I'd met at my after-school job, a college student
majoring in electrical engineering. He was a quiet and cultured young man,
but he lacked the decency to take responsibility for what had happened. The
mysterious knowledge of electricity that had attracted me to him in the first
place proved useless, and he became just another careless man who
vanished from my world.
Once my pregnancy became obvious, there was nothing I could do to
appease my mother's anger, even though we now shared the experience of
giving birth to a fatherless child. It was a melodramatic sort of anger. Her
feelings seemed to block out my own. I left home in the twenty-second
week of my pregnancy and I lost all contact with her.
When I brought my baby home from the hospital, it was to public housing
that had been set up for single mothers, and the only person who welcomed
us was the woman who served as matron for the institution. I folded up the
one picture I had saved of the baby's father and stuffed it into the little
wooden box they had given me at the hospital to hold the umbilical cord.

---

As soon as I'd managed to get the baby into a day care center, I went
straight to the Akebono Housekeeping Agency and arranged for an
interview. It was the only job I could think of that matched my limited
skills.
Shortly before Root entered elementary school, my mother and I
reconciled: a fancy backpack arrived in the mail for him. This happened at
the same time that I had left the single mothers' home and set up house for
ourselves. My mother was still managing the wedding hall. But just as our
troubles seemed to be over and I'd begun to see how comforting it could be
to have a grandmother for my child, my mother suddenly died of a brain
hemorrhage—which may be why I was even happier than Root himself
when I saw the Professor hug him.
The three of us soon fell into a pleasant routine. There was no change in my
schedule or workload, other than making more food for dinner. Fridays
were the busiest, as I had to prepare food for the weekend and store it away
in the freezer. I would make meat loaf and mashed potatoes, or poached fish
and vegetables, and explain repeatedly what went with what and how to
defrost the food, although the Professor never quite figured out how to use
the microwave. Nevertheless, when I arrived on Monday morning, all the
food I'd prepared was gone. The meat loaf and fish had somehow been
thawed and eaten, and the dirty dishes had been washed and put away in the
cupboard. I was sure that the old woman took care of the Professor when I
wasn't there, but as long as I was around, she never made an appearance. I
had no idea why she had placed such a firm restriction on communication
between her house and the Professor's, but I decided that my next challenge
was to figure out how to get to know her.
The Professor's problems, on the other hand, were all mathematical. He
never seemed particularly proud of his accomplishments, even when he had
spent a long time solving an equation that had won both the prize money
and my praise.
"It was just a little puzzle," he would say, "a game"; and his tone sounded
more sad than modest. "The person who made the problem already knew

---

the answer. Solving a problem for which you know there's an answer is like
climbing a mountain with a guide, along a trail someone else has laid. In
mathematics, the truth is somewhere out there in a place no one knows,
beyond all the beaten paths. And it's not always at the top of the mountain.
It might be in a crack on the smoothest cliff or somewhere deep in the
valley."
In the afternoon, when he heard Root's voice at the door, the Professor
came out of his study, no matter how absorbed he was in his work. Though
he had always hated to have his "thinking" interrupted, he now seemed
more than willing to give it up for my son.
Most days, however, Root simply delivered his backpack and went off to
the park to play baseball with his friends, and the Professor would retreat
dejectedly to his study.
So the Professor seemed particularly cheerful when the weather turned
rainy and he was able to help Root with his math homework.
"I think I'm a little smarter when I'm in the Professor's office," Root told
me. There were no bookshelves in the little apartment where we lived, so
the Professor's study, with its stacks of volumes lining the walls, seemed
magical to him. The Professor would sweep aside the notebooks and clips
and eraser shavings on his desk to make space for Root, and then he would
open the textbook.
How is it possible for a professor of advanced mathematics to teach a
child in elementary school? The Professor was especially gifted, he had the
most wonderful way of teaching fractions and ratios and volume, and it
occurred to me that all parents should be giving this kind of help to their
children.
Whether it was a word problem or just a simple calculation, the Professor
made Root read it aloud first.
"353 × 840 =...
"6239 ÷ 23 =...
"4.62 + 2.74 =...

---

"A problem has a rhythm of its own, just like a piece of music," the
Professor said. "Once you get the rhythm, you get the sense of the problem
as a whole, and you can see where the traps might be waiting."
And so Root read in a loud, clear voice: "I bought two handkerchiefs and
two pairs of socks for ¥380. Two handkerchiefs and five pairs of socks cost
¥710. How much did each handkerchief and each pair of socks cost?"
"So, where do we start?" asked the Professor.
"Well, it seems pretty hard."
"You're right. This is the trickiest one in your homework today, but you
read it well. The problem consists of three sentences. The handkerchiefs
and socks appear three times each, and you had the rhythm just right: so
many handkerchiefs ... so many socks ... so many yen; handkerchiefs ...
socks ... yen. You made a boring problem sound just like a poem."
The Professor was unstinting with his praise for Root. He never seemed to
lose patience when time passed and they were making little progress; and
like a miner sifting a speck of gold from the muddy river bottom, he always
found some small virtue to compliment, even when Root was stuck.
"Well then, suppose we draw a picture of this little shopping trip. First,
there are two handkerchiefs; then two pairs of socks—"
"Those aren't socks!" Root interrupted. "They look more like overweight
caterpillars. Let me draw them."
"I see what you mean. That does look more like a caterpillar." "He bought
the same number of handkerchiefs the second time but more socks. Five
pairs is a lot to draw.... Mine are starting to look like caterpillars, too."
"No, they're fine. And you're right, only the number of socks increases,
along with the price. Why don't we check to see how much the price went
up?"
"So, you'd subtract ¥380 from ¥710...."

---

"Always show your work, and do it neatly."
"I usually just scribble on the back of scrap paper."
"But every formula and every number has meaning, and you should treat
them accordingly, don't you think?"
I was sitting on the bed, doing some mending. Whenever they started
Root's homework, I tried to find something to do in the study in order to be
near them. I would iron the Professor's shirts, or work on a stain in the rug,
or snip string beans for supper. If I was working in the kitchen and heard
their laughter drift in from the other room, I felt terribly excluded—and I
suppose I wanted to be there when anyone was showing kindness to my
son.
The sound of the rain seemed louder in the study, as if the sky were
actually lower there. The room was completely private, thanks to the lush
greenery that grew up around the house, and there was no need to close the
curtains even after dark. Their reflections appeared dimly in windowpanes,
and on rainy days the musty smell in the study was stronger than usual.
"That's right! Then it's just a matter of simple division and you've got it."
"So, you get the price of the socks first: ¥110."
"Okay, but you've got to be careful now. The handkerchiefs seem
innocent, but they may turn out to be tricky."
"Right. But it's easier to do the sums when the numbers are small."
The desk was a bit too high, and Root was forced to sit up very straight as
he leaned over his problem, a well-chewed pencil clutched tightly in his
hand. The Professor sat back, legs crossed and looking relaxed, and his
hand drifted to his unshaven chin from time to time as he watched Root
work. He was no longer a frail old man, nor a scholar lost in his thoughts,
but the rightful protector of a child. Their profiles seemed to come together,
superimposed on one another, forming a single line. The gentle patter of the
rain was punctuated by the scratching of pencil on paper.

---

"Can I write out the equations separately like this? Our teacher gets mad
if we don't combine them all into one big formula."
"If you're doing them carefully and correctly, he has no reason to get
mad."
"Okay, let's see.... 110 times 2 is 220. Subtract that from 380.... That's 160
... 160 divided by 2 ... is 80. That's it. One handkerchief costs ¥80."
"That's right! Well done!"
As the Professor rubbed Root's head, Root glanced up into his face, not
wanting to miss the look of approval and pleasure.
"I'd like to give you a problem myself," said the Professor. "Would you
mind?"
"What?"
"No long faces now. Since we're studying together, I feel like playing the
teacher and giving you homework."
"That's not fair," said Root.
"It's just one little problem. All right? Here it is: What is the sum of all the
numbers from 1 to 10?"
"Okay, I'll let you give me homework if you'll do something for me. I
want you to get the radio fixed."
"The radio?"
"That's right. I want to listen to the ball games. You don't have a TV and
the radio's broken. And we're coming down to the pennant race."
"Oh, I see ... baseball." The Professor let out a long, slow breath, his hand
still resting on Root's head. "What team do you like?" he asked at last.
"Can't you tell from my hat?" Root said, picking up the cap he'd left with
his backpack and pulling it over his head. "The Tigers!"
"The Tigers? Is that right? The Tigers," the Professor murmured. "Enatsu!
Yutaka Enatsu, best pitcher of all time."

---

"Yes! Good thing you don't like the Giants. Okay, we've got to get the
radio fixed," Root insisted. The Professor seemed to be muttering
something to himself, but I closed the lid of the sewing box and stood up to
announce it was time for dinner.

---

3
I finally managed to get the Professor out of the house. Since I'd come to
work, he had not so much as set foot in the garden, let alone gone for a real
outing, and I thought some fresh air would be good for him.
"It's beautiful outside today," I said, coaxing him. "It makes you want to
go out, get some sun." The Professor was ensconced in his easy chair with a
book. "Why don't we take a walk in the park and then stop in at the
barbershop?"
"And why would we do that?" he said, glancing up at me over his reading
glasses.
"No particular reason. The cherry blossoms are just over in the park and
the dogwood is about to bloom. And a haircut might feel good."
"I feel fine like this."
"A walk would get your circulation going, and that might help you come
up with some good ideas for your formulas."
"There's no connection between the arteries in the legs and the ones in the
head."
"Well, you'd be much handsomer if you took care of your hair."
"Waste of time," he said, but eventually my persistence got the better of
him and he closed his book. The only shoes in the cupboard by the door
were old leather ones covered in a thin layer of mold. "You'll stay with
me?" he asked several times as I was cleaning them off. "You can't just
leave me while I'm having my hair cut and come home."

---

"Don't worry. I'll stay with you the whole time." No matter how much I
polished, the shoes were still dull.
I wasn't sure what to do with the notes the Professor had clipped all over
his body. If we left them on, people were bound to stare, but since he didn't
seem to care, I decided to leave them alone.
The Professor marched along, staring down at his feet, without a glance at
the blue sky overhead or the sights we passed along the way. The walk did
not seem to relax him, he was more tense than usual.
"Look," I'd say, "the cherry blossoms are in full bloom." But he only
muttered to himself. Out in the open air, he seemed somehow older.
We decided to go to the barbershop first. The barber recoiled at the sight
of the Professor's strange suit, but he turned out to be a kind man. He
realized quickly that there must be a reason for the notes, and after that he
treated the Professor like any other customer. "You're lucky to have your
daughter with you," he said, assuming we were related. Neither of us
corrected him. I sat on the sofa with the men waiting in line for their
haircuts.
Perhaps the Professor had an unpleasant memory of going to the barber.
Whatever the reason, he was clearly nervous from the moment the cape was
fastened around his neck. His face went stiff, his fingers dug into the arms
of the chair, and deep creases lined his forehead. The barber brought up
several harmless topics in an attempt to put him at ease, but it was no use.
"What's your shoe size?" the Professor blurted out. "What's your
telephone number?" The room fell silent.
Though he could see me in the mirror, he craned around from time to
time, checking to see that I'd kept my promise to stay with him. When the
Professor moved his head, the barber was forced to stop cutting, but he
would wait patiently and then go back to work. I smiled and gave a little
wave to reassure the Professor that I was still there.
The white clippings of hair fell in clumps on the cape and then scattered
to the floor. As he cut and combed away, did the barber suspect that the

---

brain inside this snowy head could list all the prime numbers up to a
hundred million? And did the customers on the sofa, waiting impatiently for
the strange old man to depart, have any notion of the special bond between
my birthday and the Professor's wristwatch? For some reason, I felt a secret
pride in knowing these things, and I smiled at the Professor just a bit more
brightly in the mirror.
After the barbershop, we sat on a bench in the park and drank a can of
coffee. There was a sandbox nearby, and a fountain and some tennis courts.
When the wind blew, the petals from the cherry trees floated around us and
the dappled sunlight danced on the Professor's face. The notes on his jacket
fluttered restlessly, and he stared down into the can as if he'd been given
some mysterious potion.
"I was right—you look handsome, and more manly."
"That's quite enough of that," said the Professor. For once he smelled of
shaving cream rather than of paper.
"What kind of mathematics did you study at the university?" I asked. I
had little confidence that I would understand his answer; maybe I brought
up the subject of numbers as a way of thanking him for coming out with
me.
"It's sometimes called the 'Queen of Mathematics,' " he said, after taking a
sip of his coffee. "Noble and beautiful, like a queen, but cruel as a demon.
In other words, I studied the whole numbers we all know, 1, 2, 3, 4, 5, 6, 7
... and the relationships between them."
His choice of the word 
queen
surprised me—as if he were telling a fairy
tale. We could hear the sound of a tennis ball bouncing in the distance. The
joggers and bikers and mothers pushing strollers glanced at the Professor as
they passed but then quickly looked away.
"You look for the relationships between them?"
"Yes, that's right. I uncovered propositions that existed out there long
before we were born. It's like copying truths from God's notebook, though
we aren't always sure where to find this notebook or when it will be open."

---

As he said the words "out there," he gestured toward the distant point at
which he stared when he was doing his "thinking."
"For example, when I was studying at Cambridge I worked on Artin's
conjecture about cubic forms with whole-number coefficients. I used the
'circle method' and employed algebraic geometry, whole number theory, and
the Diophantine equation. I was looking for a cubic form that didn't
conform to the Artin conjecture. ... In the end, I found a proof that worked
for a certain type of form under a specific set of conditions."
The Professor picked up a branch and began to scratch something in the
dirt. There were numbers, and letters, and some mysterious symbols, all
arranged in neat lines. I couldn't understand a word he had said, but there
seemed to be great clarity in his reasoning, as if he were pushing through to
a profound truth. The nervous old man I'd watched at the barbershop had
disappeared, and his manner now was dignified. The withered stick
gracefully carved the Professor's thoughts into the dry earth, and before
long the lacy pattern of the formula was spread out at our feet.
"May I tell you about something I discovered?" I could hardly believe the
words had come out of my mouth, but the Professor's hand fell still.
Overcome by the beauty of his delicate patterns, perhaps I'd wanted to take